Minimum Doublings to Reach a Threshold

Source: Phước Hưng OJ

Version: Phuoc Hung OJ Extended

Problem Statement

Given positive integers $x,t$ with $x\le t$, start from $x$. Each operation doubles the current value. Find the minimum number of operations needed to reach or exceed $t$. If the starting value already meets the threshold, the answer is zero.

Input

One line contains two integers $x$ and $t$, in this order.

Output

Print one nonnegative integer: the minimum number of doublings.

Subtasks

• Subtask 1 (20%): $1\le x\le t\le100$.
• Subtask 2 (30%): $1\le x\le t\le10^6$.
• Subtask 3 (50%): $1\le x\le t\le10^{18}$.

Examples

Example 1

Input

3 20

Output

3

Explanation

The values are 3, 6, 12, 24. Two operations are insufficient, while three reach the threshold.

Example 2

Input

100 100

Output

0

Explanation

The starting value already equals the threshold, so no operation is needed.